There are many different styles of waltz.
They are all in ¾ time ( three beats to the measure) and all are progressive, in that they travel around the room in the line of direction.
Basic ballroom waltz is based on the box step and is danced to medium/slow music with a consistent tempo .
Viennese waltz is danced to music that speeds up and slows down. It’s very fast and full of spinning turns with a lot of centrifugal force.
If you go to the Gaskills dances, from the Elizabethan era, you’ll see a lot of rotary and cross step waltz.
Rotary waltz is fast and spinning, but less complex than Viennese. Cross step is danced to slow music and as you might imagine is characterized by lots of crossing steps.
Country Western waltz resembles Viennese in it’s footwork, with the complicated arm movements of swing.
Cajun waltz zig zags around the floor similar to the Cajun Two Step.
There are other styles as well, and even I am occasionally introduced to a completely new one.
Waltz is unique in that it is the only dance that is never boring even with only the basic step. As dance historian Richard Powers pointed out in his “The Zen of Waltz” lecture, advanced dancers often prefer to simplify the waltz down to one or two simple movements. I think this is because, having no pauses, there is a hypnotic quality to the waltz, like riding a merry-go-round, that gives a trance like quality to the dance. Mesmerizing though it may be for the dancers, it’s not very interesting to watch countless turning boxes, however, so if you’re planning a waltz for your wedding you might want to add a few more steps to your routine.